Understanding and Controlling Mode Hybridization in Multicavity Optical Resonators Using Quantum Theory and the Surface Forces Apparatus

Optical fields in metal-dielectric multilayers display typical features of quantum systems, such as energy level quantization and avoided crossing, underpinned by an isomorphism between the Helmholtz and Schrödinger wave equations. This article builds on the fundamental concepts and methods of quantum theory to facilitate the understanding and design of multicavity resonators. It also introduces the surface forces apparatus (SFA) as a powerful tool for rapid, continuous, and extensive characterization of mode dispersion and hybridization. Instead of fabricating many different resonators, two equal metal-dielectric-metal microcavities were created on glass lenses and displaced relative to each other in a transparent silicone oil using the SFA. The fluid thickness was controlled in real time with nanometer accuracy from more than 50 μm to less than 20 nm, reaching mechanical contact between the outer cavities in a few minutes. The fluid gap acted as a third microcavity providing optical coupling and producing a complex pattern of resonance splitting as a function of the variable thickness. An optical wave in this symmetric three-cavity resonator emulated a quantum particle with nonzero mass in a potential comprising three square wells. Interference between the wells produced a 3-fold splitting of degenerate energy levels due to hybridization. The experimental results could be explained using the standard methods and formalism of quantum mechanics, including symmetry operators and the variational method. Notably, the interaction between square wells produced bonding, antibonding, and nonbonding states that are analogous to hybridized molecular orbitals and are relevant to the design of "epsilon-near-zero"devices with vanishing dielectric permittivity.